Hotspot Clustering

Introduction

This Jupyter Notebooks script performs k means clustering and data visualization on three data outputs from WeightedOverlayRasters, using them to make high-level planning recommendations for urban development and conservation prioritization.

Here are descriptions of the three datasets used in this analysis:

• Bio_x_Risk emphasizes areas of high land cover change probability and high biodiversity intactness.
  • Bio_x_Risk = LCC_Probability x BII
    
• Anthro_x_Risk emphasizes areas of high climate hazard probability and high human population.
  • Anthro_x_Risk = Climate_Hazards x pop2020
    
• Urban Land Cover Probability is a dataset generated using a random forest model trained on a range of physiographic factors to predict the likelihood of a raster cell to be urban in 2033.

Data Formatting

Load raster datasets and remove any NoData values that might be present

Plot datasets to be clustered

Code

# List of tuples containing raster datasets and their titles
raster_data = [
    (AnthroRisk, 'Anthropogenic Risk'),
    (BioRisk, 'Biodiversity Risk'),
    (UrbanProbability, 'Urban Probability'),
]

# Set a dark background style
plt.style.use('dark_background')

# Create a figure with 3 subplots (arranged vertically)
fig, axs = plt.subplots(3, 1, figsize=(40, 25))  # Adjust the figure size as needed

# Loop through each raster dataset and plot in subplots
for i, (data, title) in enumerate(raster_data):
    im = axs[i].imshow(data, cmap=cc.cm.bmy)  # Use a specified colormap
    axs[i].set_title(title, color='white', fontsize=30, pad=30)  # Increase the title font size and padding

    # Remove the labels on the axes
    axs[i].set_xticks([])
    axs[i].set_yticks([])

    # Create an axis for the colorbar
    divider = make_axes_locatable(axs[i])
    cax = divider.append_axes("right", size="5%", pad=0.5)

    # Add colorbar to the created axis
    fig.colorbar(im, cax=cax, orientation='vertical')

# Adjust layout to prevent overlap
plt.tight_layout()

# Display the plot
plt.show()

Merge the rasters into a single dataframe for clustering

Code

# Use the separate transform variable obtained from the data-loading function
transform = AnthroRisk_transform

# Ensure all rasters have the same shape
assert AnthroRisk.shape == BioRisk.shape == UrbanProbability.shape, "Rasters must be of the same size"

# Get coordinates
rows, cols = np.indices(AnthroRisk.shape)
xs, ys = rasterio.transform.xy(transform, rows, cols)

# Dictionary of arrays
arrays = {
    'x': np.array(xs),
    'y': np.array(ys),
    'Anthropogenic_Risk': AnthroRisk,
    'Biodiversity_Risk': BioRisk,
    'Urban_Probability': UrbanProbability
}

# Flatten the arrays
flattened_arrays = {key: value.flatten() for key, value in arrays.items()}

# Create a DataFrame
df = pd.DataFrame(flattened_arrays)

# Drop NaN values if necessary
df.dropna(inplace=True)

# df.head()

Standardize the data columns for clustering

Code

# Standardization
standard_scaler = StandardScaler()
X = standard_scaler.fit_transform(df[['Anthropogenic_Risk', 'Biodiversity_Risk', 'Urban_Probability']])

K-Means Clustering

Perform K-means clustering

Code

# Number of clusters to try out
n_clusters = list(range(2, 15))

# Run kmeans for each value of k
inertias = []
for k in n_clusters:
    
    # Initialize and run
    kmeans = KMeans(n_clusters=k, n_init=10, max_iter=600)
    kmeans.fit(X)
    
    # Save the "inertia"
    inertias.append(kmeans.inertia_)
    
# Plot it!
# Set a dark background style for the plot
plt.style.use('dark_background')

# Plotting the data
plt.plot(n_clusters, inertias, marker='o', ms=10, mfc='white', lw=4, mew=3, color='blue')

# Setting labels and title with light color for visibility
plt.title('Inertia vs Number of Clusters', color='white')
plt.xlabel('Number of Clusters', color='white')
plt.ylabel('Inertia', color='white')

# Display the plot
plt.show()

Determine the appropriate number of clusters using KneeLocator

Code

# Initialize the knee algorithm
kn = KneeLocator(n_clusters, inertias, curve='convex', direction='decreasing')

# Print out the knee 
print(kn.knee)

4

Fit the appropriate number of clusters to the data

Code

# Initialize the Kmeans object
# Using the identified knee
kmeans = KMeans(n_clusters=(kn.knee), random_state=42, n_init=10)

# Using a manually-assigned knee
# kmeans = KMeans(n_clusters=4, random_state=42, n_init=10)

# Run the fit! This adds the ".labels_" attribute
kmeans.fit(X);

# Save the cluster labels
df["cluster"] = kmeans.labels_

df.head()

	x	y	Anthropogenic_Risk	Biodiversity_Risk	Urban_Probability	cluster
0	-84.389663	10.129249	0.0	0.668739	0.000073	0
1	-84.389385	10.129249	0.0	0.665026	0.000071	0
2	-84.389107	10.129249	0.0	0.661313	0.000083	0
3	-84.388829	10.129249	0.0	0.655744	0.000098	0
4	-84.388552	10.129249	0.0	0.653149	0.000103	0

Code

# Count the number of rows for each cluster and sort them to see which clusters have the greatest number of rows
cluster_counts = df['cluster'].value_counts().sort_values(ascending=False)

# Display the counts
print('Number of Pixels per Cluster')
print(cluster_counts)
# print(df.dtypes)

Number of Pixels per Cluster
1    971354
0    924702
2    228555
3    112740
Name: cluster, dtype: int64

Make a multi-bar chart for each cluster

Code

# Group by 'cluster' and calculate mean for each column
cluster_summary = df.groupby('cluster')[['Anthropogenic_Risk', 'Biodiversity_Risk', 'Urban_Probability']].mean()

# Normalize the data
cluster_summary_normalized = (cluster_summary - cluster_summary.min()) / (cluster_summary.max() - cluster_summary.min())

# Set dark mode style
plt.style.use('dark_background')

# Define the number of groups and bar width
n_groups = len(cluster_summary_normalized)
bar_width = 0.25

# Define x coordinates for each group
index = np.arange(n_groups)
x1 = index - bar_width
x2 = index
x3 = index + bar_width

# Plotting each column in grouped bars
fig, ax = plt.subplots(figsize=(12, 6))

# Titles and colors for each plot
columns = ['Anthropogenic_Risk', 'Biodiversity_Risk', 'Urban_Probability']
colors = ['#3e208d', '#a02300', 'darkgrey']
plot_titles = ['Anthropogenic Risk Per Cluster', 'Biodiversity Risk per Cluster', 'Urban Probability per Cluster']

# Use a for loop to create each group of bars
for x, color, column, title in zip([x1, x2, x3], colors, columns, plot_titles):
    ax.bar(x, cluster_summary_normalized[column], bar_width, label=title, color=color)

# Add titles, labels, and legend
ax.set_title('Normalized Average Values per Cluster', color='white')
ax.set_xlabel('Cluster', color='white')
ax.set_ylabel('Normalized Average Values', color='white')
ax.legend()

# Set x-ticks to be in the middle of the group of bars
ax.set_xticks(index)
ax.set_xticklabels(cluster_summary.index)

# Adjust layout and show plot
plt.tight_layout()
plt.show()

Here we see how each one of the clusters is composed of a different combination of values from each of these three indicies.
Here are some high-level takeaways about the implications of each cluster.

Findings

• Land in Cluster 0 should be considered for conservation, as this means they have a high combination of land cover change probability and biodiversity.
  • No Anthropogenic Risk, High Biodiversity Risk, No Probability of Urban Land Cover
    
    
• Land in Cluster 1 can be thought of as regional landscape assets. Their low risk level makes conservation a lower prioirty, but minimizing human impact on these lands will help maintain regional biodiversity.
  • No Anthropogenic Risk, Low Biodiversity Risk, No Probability of Urban Land Cover
    
    
• Land in Cluster 2 is the most suitable for urban development out of the four clusters, since anthropogenic risk and biodiversity risk are relatively low there.
  • Low Anthropogenic Risk, Low Biodiversity Risk, High Probability of Urban Land Cover
    
    
• Land in Cluster 3 should be considered for Nature-Based Solutions (NbS) implementation, such as green stormwater infrastructure, either in the form of retrofits or included in areas of new urban development.
  • High Anthropogenic Risk, No Biodiversity Risk, High Probability of Urban Land Cover

Visualizations

Plot the clusters across space

Code

# Set the style of the visualization with a dark background
sns.set(style="darkgrid")

custom_palette = {
    0: '#cd0000',
    1: '#328232',
    2: '#A9A9A9',
    3: '#277bdb',
}

# Create a scatter plot with the custom palette
plt.figure(figsize=(10, 6))
scatter = sns.scatterplot(
    x='x', 
    y='y', 
    hue='cluster', 
    palette=custom_palette, 
    data=df, 
    s=0.5  # Point size
)

# Adding title and labels with a light color for visibility against the dark background
plt.title('K Means Clustering', color='white')
plt.xlabel('X Coordinate', color='white')
plt.ylabel('Y Coordinate', color='white')

# Change the color of ticks and labels for visibility
plt.xticks(color='white')
plt.yticks(color='white')

# Modify legend for better visibility on dark background
legend = plt.legend(title='Cluster', loc='upper right', bbox_to_anchor=(1.1, 1.05), frameon=True)
plt.setp(legend.get_texts(), color='white')  # Set the legend text color
plt.setp(legend.get_title(), color='white')  # Set the legend title color

# Set the face and edge color of the figure to match the dark theme
plt.gcf().set_facecolor('#303030')
plt.gca().set_facecolor('#303030')
plt.gca().spines['top'].set_color('white')
plt.gca().spines['bottom']. set_color('white')
plt.gca().spines['left'].set_color('white')
plt.gca().spines['right'].set_color('white')

# Display the plot
plt.show()

This plot shows two types of clusters in the urban area and two types of clusters in the non-urban area.

Code

# Sample the DataFrame at 5%
sampled_df = df.sample(frac=0.05)

# Create a 3D scatter plot using Plotly
fig = px.scatter_3d(
    sampled_df,
    x='Anthropogenic_Risk',
    y='Biodiversity_Risk',
    z='Urban_Probability',
    title='3D Scatter Plot',
    labels={
        'Anthropogenic_Risk': 'Anthropogenic Risk Index',
        'Biodiversity_Risk': 'Biodiversity Risk Index',
        'Urban_Probability': 'Suitability of Urban Land Cover',
        'cluster': 'Cluster'
    }
)

# Update marker colors and hover information directly
fig.update_traces(
    marker=dict(
        size=1.5,
        color=[custom_palette[c] for c in sampled_df['cluster']],
        opacity=0.75
    ),
    hovertemplate="Anthropogenic Risk: %{x}<br>Biodiversity Risk: %{y}<br>Urban Probability: %{z}<br>Cluster: %{customdata}"
)

# Add custom data for hover information
fig.update_traces(customdata=sampled_df['cluster'])


# Update the layout for dark mode
fig.update_layout(
    margin=dict(l=0, r=0, b=0, t=0),
    paper_bgcolor='rgb(10,10,10)',
    plot_bgcolor='rgb(10,10,10)',
    title_font_color='white',
    font_color='white',
    height=900,
    width=1600,
    scene=dict(
        xaxis=dict(
            backgroundcolor='rgb(32,32,32)',
            gridcolor='gray',
            showbackground=True,
            zerolinecolor='gray'),
        yaxis=dict(
            backgroundcolor='rgb(32,32,32)',
            gridcolor='gray',
            showbackground=True,
            zerolinecolor='gray'),
        zaxis=dict(
            backgroundcolor='rgb(32,32,32)',
            gridcolor='gray',
            showbackground=True,
            zerolinecolor='gray'),
    )
)

# Show the plot
fig.show()

This interactive plot allows us to visualize each of the factors as it varies within the cluster.
Try zooming in and rotating!